Public Vs Private Universities

college_reduced <- college %>%
select(
    CONTROL, NPT4_PUB, NPT4_PRIV,
    GRAD_DEBT_MDN10YR_SUPP, PCTFLOAN,
    PCTPELL,MD_EARN_WNE_P10
    ) %>%
  rename(
   ownership = CONTROL,
   avg_net_price.public =  NPT4_PUB,
   avg_net_price.private = NPT4_PRIV,
   median_debt_monthly_payments = GRAD_DEBT_MDN10YR_SUPP,
   federal_loan_rate = PCTFLOAN,
   pell_grant_rate = PCTPELL,
   median_salary = MD_EARN_WNE_P10
  )

college_reduced1 <- college_reduced %>%
  mutate(
  ownership = recode(
  ownership,
  `1` = "public",
  `2` = "private",
  `3` = "private"
      )
  )
# college_reduced1 %>%
#   head() %>%
#   print()

proper_type <- college_reduced1 %>% 
  mutate(
    median_debt_monthly_payments = as.numeric(median_debt_monthly_payments),
    federal_loan_rate = as.numeric(federal_loan_rate),
    pell_grant_rate = as.numeric(pell_grant_rate),
    median_salary = as.numeric(median_salary),
    avg_net_price.public = as.numeric(avg_net_price.public),
    avg_net_price.private = as.numeric(avg_net_price.private),
    ownership = as.character(ownership)
  )
# proper_type%>%
#   head() %>%
#   print()

proper_type <- proper_type %>%
  mutate(
    avg_net_price_both = case_when(
    is.numeric(avg_net_price.public) & 
    is.na(avg_net_price.private) ~ avg_net_price.public,
    is.na(avg_net_price.public) & 
    is.numeric(avg_net_price.private) ~ avg_net_price.private
        )
  )%>%
  select(
    ownership,avg_net_price.public,avg_net_price.private,
    avg_net_price_both,median_salary,federal_loan_rate,
    pell_grant_rate,median_debt_monthly_payments
  )
  # proper_type %>%
  #   print()

# Creating a new, smaller dataframe to represent income to debt ratio
# for public and private schools by subsetting of the proper_type dataframe 
Income_Debt <- proper_type %>%
  select(
    ownership,
    median_debt_monthly_payments,
    median_salary
    ) %>%
  filter(
       !is.na(median_debt_monthly_payments) &
       !is.na(median_salary) &
       (ownership == "private" | ownership == "public")
       ) %>%
  # Creating a new variable to represent income to debt ratio
  mutate(
      income_to_debt_ratio = 
      (median_salary)/(12*median_debt_monthly_payments)
        )
# Income_Debt %>%
#   head() %>%
#    print()

Box Plot of the Percentage of Students Who Received Pell Grant

proper_type %>%
  ggplot() +
  geom_boxplot(
    mapping = aes(
      x = ownership, y = pell_grant_rate, color = ownership
    )
  ) +
    labs(
      y = "Percentage of Pll Grant Recipients"
         ) + 
  theme(plot.title = element_text(size = 13, face = "bold")) + 
  theme_classic()  # Classic theme

Box Plot of the average net price for public and private schools

proper_type %>%
  ggplot()+
  geom_boxplot(mapping = aes(x = ownership, y = avg_net_price_both, color = ownership)) +
    labs(
      y = 'Average Net Price'
         ) + 
  theme(plot.title = element_text(size = 13, face = "bold")) + 
  theme_classic() 

###CDF of the mean median earnings for private and public institutions

income_cdf <-  proper_type %>%
ggplot() +
geom_step(
mapping = aes(x = median_salary, color = ownership),
stat = "ecdf"
) +
labs(
y = "CDF") +
theme(plot.title = element_text(size = 14, face = "bold")) +
    theme_classic()  # Classic theme
# + 
#   annotation_logticks() 
income_cdf

###Log-transformed CDF of the mean median earnings for private and public institutions

income_cdf <-  proper_type %>%
ggplot() +
geom_step(
mapping = aes(x = median_salary, color = ownership),
stat = "ecdf"
) +
  scale_x_log10(
     breaks = scales::trans_breaks("log10", function(x) 10^x),
   labels = scales::trans_format("log10", scales::math_format(10^.x))
  ) +
labs(
y = "CDF") +
theme(plot.title = element_text(size = 14, face = "bold")) +
    theme_classic()  # Classic theme
# + 
#   annotation_logticks() 
income_cdf

3. 4 Hypothesis Test for Median Salary of Students

college_reduced2 <- college_reduced1 %>% 
  mutate(median_salary = as.numeric(median_salary)) %>%
  filter(!is.na(ownership) & !is.na(median_salary))%>%
  select(ownership,median_salary)
public_private_summary_stat <- college_reduced2 %>% 
  group_by(ownership) %>% 
  summarize(mean_earnings = mean(median_salary)) 
public_private_summary_stat

ownership	mean_earnings
private	34659.99
public	36071.24

public_private_mean_earning <- public_private_summary_stat %>%
  pull(mean_earnings)
public_mean_earning <- public_private_mean_earning[2] 
private_mean_earning <- public_private_mean_earning[1]

diff_in_mean_earnings <- public_mean_earning - private_mean_earning
cat("The observed value", diff_in_mean_earnings, sep = " = $")

## The observed value = $1411.257

public_private_mean_earnings_null <- college_reduced2 %>% 
  specify(formula = median_salary ~ ownership) %>% 
  hypothesize(null = "independence") %>% 
  generate(reps = 10000, type = "permute") %>% 
  calculate(stat = "diff in means", order = combine("public", "private")) 

public_private_p_value_two_sided <- public_private_mean_earnings_null %>%
  get_p_value(obs_stat = diff_in_mean_earnings, direction = "both")
public_private_p_value_two_sided

p_value
0.0022

public_private_mean_earnings_null %>% 
  visualize() + 
  shade_p_value(obs_stat = diff_in_mean_earnings, direction = "both")+ 
  labs( x = "difference in means", 
  title = "Difference in mean earnings null distribution" ) + 
  theme(plot.title = element_text(size = 8, face = "bold"))

3.5 Using the 95% Confidence Interval

public_private_mean_earnings_bootstrap <- college_reduced2 %>% 
  specify(formula = median_salary ~ ownership) %>%
  generate(reps = 10000, type = "bootstrap") %>% 
  calculate(stat = "diff in means", order = combine("public", "private")) 

public_private_mean_earnings_ci95 <- public_private_mean_earnings_bootstrap %>%
 get_confidence_interval()
public_private_mean_earnings_ci95

2.5%	97.5%
583.6245	2259.569

public_private_mean_earnings_bootstrap %>% 
  visualize() + 
  shade_confidence_interval( endpoints = public_private_mean_earnings_ci95 ) + 
  labs( x = "difference in median means",
  title = "Difference in mean median earnings 95% confidence interval" )+    
  theme(plot.title = element_text(size = 8, face = "bold"))

###Histogram of the Debt Ratio of Students Working and Not Enrolled 10 Years After Entry

hist_plot <- Income_Debt %>%
  ggplot() +
  geom_histogram(mapping = 
  aes(income_to_debt_ratio, fill = ownership),alpha = 0.5, binwidth  = 6
  )+
 scale_x_continuous(breaks = seq(0,300,25)) +
  labs(
x = 'Income to debt Ratio', y = "Proportion") +
theme(plot.title = element_text(size = 13, face = "bold"))
hist_plot

###Income to debt Ratio of Students Working and Not Enrolled 10 Years After Entry

density_plot <- Income_Debt %>%
  ggplot() +
  geom_density(mapping = 
  aes(income_to_debt_ratio, color = ownership),alpha = 0.5
  )+
 scale_x_continuous(breaks = seq(0,300,25)) +
  labs(
x = 'Income to debt Ratio', y = "Proportion") +
theme(plot.title = element_text(size = 13, face = "bold"))
density_plot <- ggplotly(density_plot)
density_plot

###Income to debt Ratio of Students Working and Not Enrolled 10 Years After Entry

###Scatter Plot of Median Income Versus Yearly Debt Payments 10 Years after Entry to Institution

dept_income_plot <- Income_Debt %>%
  ggplot(
    mapping = 
  aes(y = median_salary, x = median_debt_monthly_payments*12,
      shape = ownership,color = ownership),alpha = 0.3
  ) +
  geom_point() +
  labs(
       x = 'Median Yearly Debt Payments',
       y = 'Median Salary')+
    scale_x_log10() +
    scale_y_log10()+
  theme(plot.title = element_text(size = 15, face = 'bold')) +
    theme_classic() 
# Adding a horizontal and a vertical reference lines
  dept_income_plot + geom_hline(yintercept = (3*10**4),
             linetype = 2, color = 'red', size = 2)+
    geom_vline(xintercept = (1500),
             linetype = 2, color = 'green', size = 2)

3.8 Types of Degree Programs Offered

# Categorizing various degree programs as one of four categories
degree_programs_rate <-  college %>%
  transmute(
    CONTROL, # Ownership variable
    
    # Below are the variable names that are given in the original dataframe
    # The variable names are not user friendly, so I change them in the rename fucntion 
    
    
    # List of degree programs considered as Business and Law
    PCIP01, PCIP03, PCIP04, PCIP05,
    
    # List of degree programs considered as STEM
    PCIP43, PCIP44, PCIP45, PCIP46, PCIP47, PCIP48, 
    PCIP49, PCIP50, PCIP51, PCIP52, PCIP54,
    
    # List of degree programs considered as Humanities
    PCIP09, PCIP10, PCIP11, PCIP12, PCIP13, 
    PCIP14,PCIP15, PCIP16, PCIP19, PCIP22,
    PCIP23, PCIP24, PCIP25, PCIP26, PCIP27,
    
    # List of degree programs considered as other
    PCIP29, PCIP30, PCIP31, PCIP38,
    PCIP39, PCIP40, PCIP41, PCIP42
    
  ) %>%
  rename( # Renaming all the Variables
    
    ownership = CONTROL,
    
    # Bussiness and Law
    percentage_agriculture =  PCIP01,
    percentage_resources = PCIP03,
    percentage_architecture = PCIP04,
    percentage_ethnic_cultural_gender = PCIP05,
    
    # STEM
    percentage.security_law_enforcement = PCIP43,
    percentage.public_administration_social_service = PCIP44,
    percentage.social_science   = PCIP45,
    percentage.construction = PCIP46,
    percentage.mechanic_repair_technology = PCIP47,
    percentage.precision_production = PCIP48,
    percentage.transportation   = PCIP49,
    percentage.visual_performing    = PCIP50,
    percentage.health   = PCIP51,
    percentage.business_marketing   = PCIP52,
    percentage.history  = PCIP54,
    
    # Humanities
    percentage.communication = PCIP09,
    percentage.communications_technology = PCIP10,
    percentage.computer = PCIP11,
    percentage.personal_culinary = PCIP12,
    percentage.education =  PCIP13,
    percentage.engineering = PCIP14,
    percentage.engineering_technology = PCIP15,
    percentage.language = PCIP16,
    percentage.family_consumer_science = PCIP19,
    percentage.legal =  PCIP22,
    percentage.english = PCIP23,
    percentage.humanities = PCIP24,
    percentage.library =  PCIP25,
    percentage.biological = PCIP26,
    percentage.mathematics = PCIP27,
    
    # other
    percentage.military = PCIP29,
    percentage.multidiscipline = PCIP30,
    percentage.parks_recreation_fitness = PCIP31,
    percentage.philosophy_religious = PCIP38,
    percentage.theology_religious_vocation = PCIP39,
    percentage.physical_science = PCIP40,
    percentage.science_technology = PCIP41,
    percentage.psychology = PCIP42
    
  ) %>%
  mutate( # Giving the Proper Data Types for all the Variables
  ownership = recode(
  ownership,
  `1` = "public",
  `2` = "private",
  `3` = "private"
      ),
  # Adding the proportionl value of all degree programs considered as Business and Law
    percentage_agriculture =  as.numeric(percentage_agriculture),
    percentage_resources = as.numeric(percentage_resources),
    percentage_architecture = as.numeric(percentage_architecture),
    percentage_ethnic_cultural_gender = as.numeric(percentage_ethnic_cultural_gender),
  
  # Adding the proportionl value of all degree programs considered as STEM 
  percentage.security_law_enforcement   = 
  as.numeric(percentage.security_law_enforcement),
  percentage.public_administration_social_service   = 
  as.numeric(percentage.public_administration_social_service),
  percentage.social_science = 
  as.numeric(percentage.social_science),
  percentage.construction   = 
  as.numeric(percentage.construction),
  percentage.mechanic_repair_technology =   
  as.numeric(percentage.mechanic_repair_technology),
  percentage.precision_production   = 
  as.numeric(percentage.precision_production),
  percentage.transportation = 
  as.numeric(percentage.transportation),
  percentage.visual_performing  = 
  as.numeric(percentage.visual_performing),
  percentage.health = 
  as.numeric(percentage.health),
  percentage.business_marketing = 
  as.numeric(percentage.business_marketing),
  percentage.history    = 
  as.numeric(percentage.history),
  
  # Adding the proportionl value of all degree programs considered as Humanities
  percentage.communication = 
  as.numeric(percentage.communication),
  percentage.communications_technology = 
  as.numeric(percentage.communications_technology),
  percentage.computer = 
  as.numeric(percentage.computer),
  percentage.personal_culinary = 
  as.numeric(percentage.personal_culinary),
  percentage.education =  
  as.numeric(percentage.education),
  percentage.engineering = 
  as.numeric(percentage.engineering),
  percentage.engineering_technology = 
  as.numeric(percentage.engineering_technology),
  percentage.language = 
  as.numeric(percentage.language),
  percentage.family_consumer_science = 
  as.numeric(percentage.family_consumer_science),
  percentage.legal =  
  as.numeric(percentage.legal),
  percentage.english = 
  as.numeric(percentage.english),
  percentage.humanities = 
  as.numeric(percentage.humanities),
  percentage.library =  
  as.numeric(percentage.library),
  percentage.biological = 
  as.numeric(percentage.biological),
  percentage.mathematics = 
  as.numeric(percentage.mathematics),
  
  # Adding the proportionl value of all degree programs considered as Other
  percentage.military = 
  as.numeric(percentage.military),
  percentage.multidiscipline = 
  as.numeric(percentage.multidiscipline),
  percentage.parks_recreation_fitness = 
  as.numeric(percentage.parks_recreation_fitness),
  percentage.philosophy_religious = 
  as.numeric(percentage.philosophy_religious),
  percentage.theology_religious_vocation = 
  as.numeric(percentage.theology_religious_vocation),
  percentage.physical_science = 
  as.numeric(percentage.physical_science),
  percentage.science_technology = 
  as.numeric(percentage.science_technology),
  percentage.psychology = 
  as.numeric(percentage.psychology)
  
  ) 

degree_programs_rate <- degree_programs_rate %>%
  mutate(
    # Total Percentage for Business and Law
    total_bus_law = (
    percentage_agriculture +
    percentage_resources +
    percentage_architecture + 
    percentage_ethnic_cultural_gender),
    
    # Total Percentage for STEM
   total_stem = (
    percentage.security_law_enforcement + 
    percentage.public_administration_social_service +
    percentage.social_science   +
    percentage.construction +
    percentage.mechanic_repair_technology +
    percentage.precision_production +
    percentage.transportation   +
    percentage.visual_performing +
    percentage.health   +
    percentage.business_marketing   +
    percentage.history),
    
    # Total Percentage for Humanities
    total_humanities = (
    percentage.communication +
    percentage.communications_technology +
    percentage.computer +
    percentage.personal_culinary +
    percentage.education +
    percentage.engineering +
    percentage.engineering_technology +
    percentage.language +
    percentage.family_consumer_science +
    percentage.legal +
    percentage.english +
    percentage.humanities +
    percentage.library +
    percentage.biological +
    percentage.mathematics),
    
    # Total Percentage for Other Degree Programs
    total_others = (
    percentage.military +
    percentage.multidiscipline +
    percentage.parks_recreation_fitness +
    percentage.philosophy_religious +
    percentage.theology_religious_vocation +
    percentage.physical_science +
    percentage.science_technology +
    percentage.psychology)
  )
  
# degree_programs_rate %>%
#   head()  %>%
#   print()

degree_types_percentage <-  degree_programs_rate[,c('ownership','total_bus_law',
                                'total_stem','total_humanities','total_others')]
degree_proportion_table <-  degree_programs_rate %>%
  group_by(ownership) %>%
  summarize(
    bus_and_law = mean(total_bus_law, na.rm = T),
    stem = mean(total_stem, na.rm = T),
    humanities = mean(total_humanities, na.rm = T),
    others = mean(total_others, na.rm = T),
    toal = bus_and_law + stem + humanities + others
  )
#degree_proportion_table 

Degree Proportions Offered by Public Schools

proportion_public <- subset(degree_proportion_table,
                           ownership == 'public', select = c(-1,-6))
proportion_public <- as.numeric(c(proportion_public))
name = c("bus_and_law","stem",'humanities','others')
lbls <- paste(name,' ',round(proportion_public*100,2),'%')
pie(proportion_public,labels=lbls)

Degree Proportions Offered by Private Schools

proportion_private <- subset(degree_proportion_table,
                           ownership == 'private', select = c(-1,-6))
proportion_private <- as.numeric(c(proportion_private))
name = c("bus_and_law","stem",'humanities','others')
lbls <- paste(name,' ',round(proportion_private*100,2),'%')
pie(proportion_private,labels=lbls)